Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
304 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×Dic20 | C2 | semidirect |
| 4. C5×#3950 | C2 | semidirect |
| 5. #11716606 | C2 | semidirect |
| 30. C2×Dic20 | D5 | semidirect |
| 37. #3950 | D5 | semidirect |
| 42. C2×C5⋊D5 | Q16 | semidirect |
| 109. C52 | #467 | semidirect |
| 168. C5 | #65176 | semidirect |
| 169. C5 | #65477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C5⋊D5 | 2 |
| C2×C5×Dic20 | 2 |
| #11716990 | 2 |
| C5×#3950 | 2 |
| #11716606 | 2 |
| #65477 | 5 |
| #65176 | 5 |